Overtopping resistant dikes

This article is a summary of the report by Van der Meer et al. (2010).

Many studies have been devoted to this topic since, showing:

• Erosion of the inner slope by overtopping waves is a major cause of dike failure.
• The quality of the grass cover of the inner dike slope is key for the resistance to overtopping waves. A degraded grass cover can increase the failure risk by a factor 10 - 100.
• Overtopping waves create flow pulses with a high initial velocity over the inner dike slope. Because high velocities over the slope are far more damaging than low velocities, infrequent overtopping high waves cause more damage than frequent overtopping low waves.
• The highest stresses generally occur at the toe of the inner dike slope. Big waves may separate from the bed when overtopping onto a steep inner slope. In this case most damage occurs at the point where the wave reattaches to the slope.

Introduction

In 1953 the Netherlands experienced a major flooding. Studies determined that most of the dike breaches were caused by overtopping (and even overflowing) of the dikes; failure started at the landward slope of the structures. At that time, all dikes had a rather low crest and were built with a steep landward slope. Since then all major water defences were raised and the landward slopes were made more gentle. The dikes in the western part of the Netherlands were raised such that overtopping rates exceeding 0.1 l/s per meter would have a probability not greater than 1/10,000 per year. In the 1990ties it was decided by law that all major water defences should be periodically assessed for safety (periodicity of about 6 years). In the first safety assessment it was found that a large number of dikes had to be raised again in order to comply with the safety standards. This prompted the question if the method to determine the rate of wave overtopping was correct or not. Also the question was put forward if the safety standard of 0.1 l/s per meter with a 1/10,000 probability was adequate. It turned out that the flooding mechanisms were not understood well enough and that the safety standard was wrongfully determined on basis of testing with overflow instead of overtopping. Additionally, failure mechanisms were not adequately described. This lead to a Dutch national research program on loads on and strength of flood defences. To assess the erosion strength of grass covers on inner slopes and transition zones between slope to horizontal flats, destructive tests using a Wave Overtopping Simulator were performed at several dikes in the Netherlands. This Wave Overtopping Simulator (see Fig. 3) performs destructive tests on inner slopes of real dikes in order to establish the erosion resistance against overtopping waves from severe storms.

Definition, design and function

Dikes and levees are applied wherever a hinterland needs protection against flooding. These protection measures prevent an area from flooding thus providing safe conditions for economic and social activities. The dikes are designed in such a way that they are geotechnically stable under normal and extreme conditions. Dutch dikes are designed to avoid overtopping, but no overtopping cannot be guaranteed. The structures which are described here are mainly dikes with grass-covered inner (landward) slopes such as the ones found in the Netherlands. They are mostly made with a sand core covered by a clay layer on the slopes and the crest.

Figure 1: Cross section of a Dutch seadike

The typical geometry of dikes and levees is an outer or seaward slope then a crest and then a landward slope (right-hand side of Figure 1). The function of the landward slopes is to ensure stability of the dike structure and to guide overtopping waves or water flowing over the crest to the inlands. The landward slopes must be able to resist loads induced by design conditions. The slope angles as well as the width of the crest vary. In the Dutch case, sea dikes have a typical landward slope 1v:3h. River dikes are mostly steeper, up to 1v:2h. The height of the dikes is also highly variable. It depends on the local hydraulic conditions and on the norm frequency of water level for which the dike is designed. This varies from 1/10,000 per year for sea defences in the western part of the Netherlands to 1:1,250 years for dikes along rivers.

Dikes and levees protect up to a certain level. Absolute safety is impossible. The level to which a dike or a levee protects from flooding depends on the hydraulic regime, the physics of the structure (geometric and geotechnical) and the intended risk reduction or allowable risk to which it is designed. This implies that an economic optimum (or in some cases the availability of funds) defines the achievable level of risk reduction. More than half of the Netherlands is below sea level and therefore has to be protected by dikes or other flood protection structures (including dunes). The dikes in the Netherlands are currently designed based on exceedance of a certain water level that is extrapolated from a long time series (over 200 years) and scientific hindcasting. From these water levels, corresponding wave action is calculated. The combination of water level and hydraulic conditions determines the design conditions. Back in 1956, the first Delta Committee already did some early calculations and concluded that the level of protection of the western part of the Netherlands should be higher than in other parts (highest economic value). They found that this part should have a protection level (based on exceedance of water level) of 1/100,000 per year. They knew dikes to have a large residual strength in the designs. They assumed this to be a factor 10 resulting in lowering the norm to once in ten thousand years. In 1996 the safety levels in the Netherlands were registered in the Water Defence Act. In 2009 this Act was replaced by the Water Act. In the Act of 1996 it was stated that the basis for the safety standards should be transformed from exceedance of a certain water level to a risk based approach.

Experimental experience with function and performance

Onset

The landward slope of dikes proved a weak spot during the flooding of 1953 in the Netherlands (over 1,800 people drowned). Back then the dikes were much lower than today. This event led to the Delta Plan recommended heightening the dikes and to reduce the landward slopes to 1:3 or even milder to mitigate the erosive impact of overtopping waves. Before 1953 the landward slopes were very steep, 1:2 or even steeper. Another example is the impact of hurricane Katrina on New Orleans where many landward slopes failed before the water level reached the crest of the levees. Water coming over the dikes or levees does not necessarily mean danger. If the area can cope with a certain amount of water without causing any or just minor socio-economic damage, it may be acceptable. To optimize costs and competition for space, the dimensions needed for flood protection is preferably limited. Allowing some water passing the crest of the dike by overtopping waves implies that the need to heighten (and widen) the dikes decreases. If the dikes are strong enough and the amount of overtopping water can be handled, the design level of the structure can be lowered. However, the effect of overtopping water passing the crest of dikes was not well known.

Figure 2: Principle of the Wave Overtopping Simulator. From Van der Meer 2008.

From 2006 and onward, Wave Overtopping Simulators (see Figs. 2 and 3) were applied at 19 sections of dikes at 6 different locations in the Netherlands. Destructive tests have shown the behaviour of various inner slopes of dikes, embankments or levees under simulated of wave overtopping, up to a mean overtopping discharge of 125 l/s per m. Some results are presented in the following. Until 2009 overtopping tests with the overtopping simulator have been performed on real Dutch dikes, with hydraulic loads consistent with more or less general extreme sea conditions along the Dutch coast (H_s = 2 m). The tests performed in 2010 were located along a river dike but the hydraulic loads induced were from a sea dike (H_s = 1-3 m). The main reason for this choice was the fact that this dike had a very high sand content (85 and 95%) compared to clay-covered dikes more commonly found along the Dutch sea coast. The core of the dikes is usually sand although in some cases the core of the dike is bolder clay. The cover layer on the landward slopes of sand dikes is typically 0.6 m thick. The thickness of the cover on the sea side is mostly 1 m. In the test locations we indeed found clay covers on the landward slope mainly in the range of 0.6 m but also a location where the thickness of the clay cover only was 0.4 m was found.

Test results

Figure 1: Release of a wave from the simulator. From Van der Meer 2008.

The process of wave overtopping on dikes and levees is fairly well known (Overtopping Manual, 2018). In contrast, the erosive impact of wave overtopping is not well known, mainly due to the fact that research on this topic cannot be performed on a small scale, as it is practically impossible to scale clay and grass down properly. Only some tests have been performed in large wave flumes, like the Delta flume in the Netherlands and the GWK in Germany, see Smith (1994) and Oumeraci et al. (2000). Therefore, the Wave Overtopping Simulator has been developed; see Van der Meer et al. (2007 and 2010) for more details. The Simulator consists of a high-level mobile box to store water. The maximum capacity is 5.5 m³ per m width (22 m³ for a 4 m wide Simulator). This box is continuously filled with a predefined discharge and emptied at specific times in such a way that it simulates the overtopping tongue of a wave at the crest and inner slope of a dike, see Fig. 3. The discharge of water is released in such a way that for each overtopping volume of water the flow velocity and thickness of the water tongue at the crest corresponds with the characteristics that can be expected for real wave overtopping under extreme storm conditions.

Figure 4: Distribution of overtopping volumes of waves for sea dikes and various mean overtopping discharges, as simulated by the Wave Overtopping Simulator, based on Hs = 2 m and wave steepness 0.04 (peak period). From Van der Meer 2008.

Field tests have been carried out at the end of the winter when grass roots are in their worst condition. The design and calibration of the Wave Overtopping Simulator are described by Van der Meer (2007) and the test results of the first tested dike are described by Akkerman et al. (2007). Part of the tests in 2008 were presented by Steendam et al. (2008). A summary report of all the tests was written by Van der Meer et al. (2010). Each test condition was characterised by a mean discharge and lasted for 6 hours. Test conditions increased from 0.1 l/s per m to 1; 5; 10; 30; 50 and 75 l/s per m. A full test on a dike section took about one week and often more than 14,000,000 litres of water flowed over the inner slope of 4 m width. Each test condition consisted of simulation of the required distribution of overtopping volumes (Overtopping Manual, 2018). Such a distribution depends on expected conditions at sea: a larger significant design wave height (and corresponding higher dike) will show fewer overtopping waves, but the volume in the overtopping waves will be bigger than for a smaller significant design wave height (and corresponding lower dike). All tests until 2009 have assumed a significant wave height of 2 m with a wave steepness of 0.04 (using the peak period). Distributions of overtopping volumes for this condition and for various mean discharges are given in Figure 4. In 2010 also tests have been performed with a significant wave height of 3 m and 1 m.

Figure 4 shows that for each mean overtopping discharge only a relatively small number of waves (the largest ones at the right of each graph) produce large overtopping volumes. The general behaviour of wave overtopping can be described by a large number of fairly small overtopping waves and a few which are much bigger. These few but bigger waves often cause the damage to the inner slope. A floating device was used to measure the flow depth and a high speed camera to measure front velocities of an overtopping wave. The maximum flow depth is about 0.25 m. The velocities can approach 8 m/s and the water is very turbulent with a lot of air entrainment, estimated to be about 10%). Wave overtopping may lead to failure of the crest and inner slope of a dike. In principle there are two different failure mechanisms. Fast overtopping water may damage the surface of the crest and inner slope and, if initial damage or erosion has occurred, this may continue to the layer underneath the grass cover and may lead to an initial breach. This is actually the process which is simulated by the Wave Overtopping Simulator: erosion of the slope. A major failure mechanism on steep inner faces (typically 1:1.5 and 1:2) in the past was slip failure of the (rear) slope. Such slip failures may lead directly to a breach. For this reason most dike designs in the Netherlands in the past fifty years have used a 1:3 inner slope, where it is unlikely that slip failures will occur due to overtopping. This mechanism might however occur for inner slopes steeper than 1:3 and should then be taken into account in safety analysis. This failure mechanism is not simulated by the overtopping tests, as a slip failure needs more width to develop than the 4 m wide test section.

Figure 5: Example of damage by the wave overtopping simulation. From Van der Meer 2008.

Inner slopes of a dike, covered with grass on clay, never failed by overtopping wave erosion for a mean overtopping discharge of 30 l/s per m or less. Only one section failed at 50 l/s per m; some although not all at 75 l/s per m (example Fig. 5). Large erosion resistance of the inner slope of a dike is determined by the combination of grass and clay. The grass cover seems stronger if it grows on sandy clay and may even resist up to 75 l/s per m. But if significant damage occurs, the clay layer is not very erosion resistant. Since grass roots can barely penetrate good quality clay, no strong grass cover could be found. Here grass may rip off for overtopping discharges around 30 l/s per m although the remaining good quality clay layer, still reinforced with some roots, has a large erosion resistance against overtopping waves. Therefore a good grass cover on a sandy clay and a worse grass cover on good clay show different failure mechanisms but similar strength against wave overtopping. Thus the grass sod and its way of maintenance may have less influence on the total strength than previously anticipated. Bad grass coverage (small open areas without grass) on sandy clay may show less resistance. Transitions from slope to horizontal such as the transition from the inner slope to the toe of the dike are probably the most critical locations for initial and increasing damage. Damage here was initiated by a mean discharge of 10 l/s per m or more. As the damage occurred at the lowest part of the inner slope it will take time for damage to extend to the crest level and subsequently cause a dike breach. Transitions higher on the inner slope might be more critical. A hole in the layer of clay created at a large mean overtopping discharge of 50 l/s per m or more which reaches the under laying sand core, will give a very quick ongoing erosion. Although a test with a parking place of bricks showed that sand erosion at 10 l/s per m or more is very fast (the experiment was even stopped at 30 l/s per m due to fast ongoing damage to the parking area) the dike itself was not in danger at all. Small obstacles like poles and fences did not show any erosion. Small holes from mice and moles did not initiate damage to the grass cover layer. An obstacle like a concrete staircase on the inner slope was totally destroyed at a stage with 75 l/s per m overtopping but the dike itself was not in danger.

Modelling of wave overtopping rates

Modelling of wave overtopping at breakwaters, dikes and seawalls is dealt with in the articles:

• Modelling coastal hydrodynamics
• Hydrodynamic numerical models of wave-structure interaction

Eurotop manual

A review of methods for determining wave overtopping rates at structures in the surf zone is presented in the EurOtop manual 2018 . Empirical formulae are given for various types of structures and examples are shown of damage occurring as a consequence of wave overtopping.

Related articles

• Stability of rubble mound breakwaters and shore revetments

References

The main authors of this article are De Rijcke, Maarten, Steendam, Gosse Jan, Zanuttigh, Barbara, Prinos, Panayotis, Lopez, Lara and Andersen, Thomas Lykke Please note that others may also have edited the contents of this article. For other articles by this author see Category:Articles by De Rijcke, Maarten